A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was rated to carry 70 passengers (so the load limit was 9,660 lb). After the boat sank, the assumed mean weight for similar boats was changed from 138 lb to 172 lb. Complete parts a and b below. 3 Part Question... Part 1 A. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 178.1 lb and a standard deviation of 37.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 138 lb. The probability is (Blank). (Round to four decimal places as needed.) Part 2 B. The boat was later rated to carry only 16 passengers, and the load limit was changed to 2,752 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 (so that their total weight is greater than the maximum capacity of 2,752 lb). The probability is (Blank). (Round to four decimal places as needed.) Part 3 C. Do the new ratings appear to be safe when the boat is loaded with 16 passengers? Choose the correct answer below. A. Because 178.1 is greater than 172, the new ratings do not appear to be safe when the boat is loaded with 16 passengers. B. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 16 passengers. C. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 16 passengers. D. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A boat capsized and sank in a lake. Based on an assumption of a
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